## New answers tagged order-theory

3
votes

Accepted

### Posets of equational theories of "bad quotients"

Let $\mathbb{R}=(\{\textrm{real numbers}\};0,1,+,\times)$. Is there an equivalence relation $E$ on $\mathbb{R}$ such that $\mathbb{P}_\mathbb{R}(E)$ is not upwards-directed?
I will assume that the ...

3
votes

Accepted

### Sizes of linearly ordered subalgebras of powers

Yes, and you can find them included in your infinite linear subpower. The variety $V$ generated by a finite algebra $\mathcal A$ (which includes all subpowers) is locally finite, i.e., finitely ...

1
vote

Accepted

### Large Borel antichains in the Cantor cube?

The answer to the More Precise Question is yes. Define
$$B_n=\{f\in 2^\omega:f(i)\neq f(2^n+i)\text{ for all }0\leq i<2^n\}$$
$$C_n= \{f\in 2^\omega:f(i)= f(2^n+i)=0\text{ for some }0\leq i<2^n\}...

2
votes

### Does strong stochastic ordering exist?

First, for the discrete topology, $U := \{\mu\}$ and $V := \{\nu\}$ are open and have the property wanted. Surely this is excluded. For the weak convergence topology, the Wasserstein metric and the ...

2
votes

Accepted

### Does strong stochastic ordering exist?

You could define a distance on probability measures by the smallest $c$ such that there exists a coupling giving mass $1$ to a $c$-neighbourhood of the diagonal. Many pairs would be infinite distance ...

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